P=NP eching

$$P = N P$$

N uchun yechish

$$\left\{\begin{matrix}\\N=1\text{, }&\text{unconditionally}\\N\in \mathrm{R}\text{, }&P=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$NP=P$$

Tenglama standart shaklda.

$$PN=P$$

Ikki tarafini P ga bo‘ling.

$$\frac{PN}{P}=\frac{P}{P}$$

P ga bo'lish P ga ko'paytirishni bekor qiladi.

$$N=\frac{P}{P}$$

P ni P ga bo'lish.

$$N=1$$

P uchun yechish

$$\left\{\begin{matrix}\\P=0\text{, }&\text{unconditionally}\\P\in \mathrm{R}\text{, }&N=1\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan NP ni ayirish.

$$P-NP=0$$

P'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(1-N\right)P=0$$

0 ni 1-N ga bo'lish.

$$P=0$$